D20 vs Spin Down Die

Can your MTG Spindown Die replace a standard D20? Let's do the math to find out once and for all!

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[AwkwardJameschannel]

Local man saves $500 dollars by buying a mirror instead of another camera. Produces same results.

[OrdinarilyBob]

Anyone smart enough to use the mirror in this way deserves my subscription [SUBSCRIBED]. Cool vid, too.

[alexanderbarlow]

I did the experiment with 54 rolls (each) and similarly my results were:
D&D dice: 11.1
MtG dice: 10.8

[TakaAmun]

Perhaps someone already mentioned it, but if you just want to assess physical die balance due to flaws or construction...
A simple saltwater floating test would do the trick. drop the die in, give it a little spin, see if the high numbers come to surface more frequently. You will need to do this at least 25 times to determine if there's an internal flaw (air bubble, weight displacement) or construction flaw (material imbalance due to the lesser surface material of multiple, double digit numbers in the upper sphere of the die, with dense side settling on bottom of float)

[JohnnyYeTaecanUktena]

Honestly you should be using a dice tower to roll them anyways as the problem with spin downs are not that they are not random as they are as random as a D20 when you roll them with a very slight difference that is not noticeable the problem is that spin downs are easy to cheat with if people are not using Dice Towers or rolling them against a mini wall which negates any form of trying to cheat which is why in a lot of casino games they have you roll dice against the walls. So unless you have a DIce Tower it is best to stick to a D20

[Volvandese]

I tried this out not long ago with 50 rolls each from a dozen d20s and spindowns. Like for you, there was essentially no difference between the results of the two types.

I suppose a wildly out-of-balance spindown would have a higher divergence, but honestly I think many of us tend to overestimate the frequency (and degree) of manufacturing balance flaws.

[byronlee]

When it comes to the spin down d20 dice, I do have several. But I use them for keeping track of hit points instead of using them for my dice rolls.

[tobistein]

For a perfectly fair 20 sided die, the expected average roll value is 10.5 and the average chance a given side is rolled is 0.05.

There is an assumption here that the "fairness" of a die is determined by the average roll. I think a better definition of fairness is that each side has an equal probability of being rolled. Using that definition of fairness, the average roll value isn't the best way to determine if a die is fair or not. You could roll nothing but 16s and 8s and get a 10.5 average. It tells you nothing about the frequency with which a single side is rolled. That frequency tells us about the spread of probabilities to roll any given side. This can also tell you in what direction and to what magnitude the center of mass of the die is pointed away from its geometric center (this is what causes a die to be weighted). Let's call that "lean" from now on.

Because of the way d20s are designed, with one side having the "inverse" value of its opposite side and essentially randomizing which sides neighbor which (there's no agreed upon standard), lean in a given direction will have a less powerful impact on the average roll value. HOWEVER, not all sides are created equal! Certain sides have extra effects, like 20 and 1 (and 19 and 18 if you're a Champion Fighter or have certain magic items). A lean away from or towards 20 can have more significant effects on fairness because it affects the rate of critical successes and failures. Some features also have different effects if the same side is rolled multiple times, which is more likely when a die has lean. All of the above are reasons why the frequency of rolling a given side is more important than the average value in determining dice fairness for use in TTRPGs.

The fact that only one die of each type was used doesn't help with the quality of this experiment. His d20 rolled further from fair than his Spindown die. Sample size of 1 for each type. There is very little statistical confidence that this is indicative of the fairness of either type of die in general. If, for instance, his Spindown has no lean but his d20 does (which we have no way of knowing), then his Spindown will likely be closer to fair anyway.

In order to come to a confident, general conclusion about the fairness of d20s vs Spindown dice, you would need a large number of each type of die. You would need to roll each die more times than he rolled these two. You would need to take into account additional variables like manufacturer, material of the die and surface being rolled on, font and depth of number engravings, external physical imperfections, and even the method of rolling the die. All of this to determine the general relative fairness of one configuration of numbers vs another.

Personally, I don't think this experiment is worth pursuing. Use whatever kind of 20-sided die you like. If it really matters to you, I'd suggest that you get a dice box so you're rolling on the same surface you'd use while playing and test your dice individually. Calculate the frequency of rolling each side vs the expected value (# side rolled / # total rolls / 0.05 * 100%) and see if there's a pattern for some sides rolling further from 100%. No die will be perfect, but some will be closer to perfect than others.

TL;DR
Spindown vs d20 in general doesn't really matter. If you really care about your dice being fair, just test them.

[SasmakToy]

I love this. Thank you! I am getting into dicemaking and clicked your video to see if there is a general preference for d20's over spindowns. However, I only have spindowns on hand right now, so seeing this attests to the idea that I can mold and cast spindowns without worrying about the arrangement of the pips.

[Fausto_]

i never understood why anyone cares, we're just rolling to see who goes first in commander. if you want to go first that bad just say so and i'll let you.

[JonSteitzer]

Great video, excellent science based approach. I thoroughly enjoyed this and appreciate the time you put into this.

[ReMeDy_TV]

While this is great data, one thing that is overlooked is the MtG spindown was rolled fairly; conduct the test through the eyes of a cheater by weak rolling the spindown. Consider it a challenge: See how much you can skew the 10.7 avg data. Also, most players use playmats, so the dice will land on a softer surface rather than a hard table.

MtG players will need to be vigilant of opponents weak rolling their dice in the future with the latest D&D cards.

[chortlesinthecorner]

So glad someone did this! Kind of glad the result was basically a tie since I never felt it was that big of a deal haha(at least for determining who goes first in Magic). If someone is trying to cheat the spindown gives far greater opportunity, but it has less to do with differing weight(real weighted dice are almost like magnets) and more to do with roll velocity/surface type/starting position. For MTG it presents a rather limited issue, but for D&D it's a core part of the game so I can see where even if it's mathematically inconsequential using a spindown creates far too much opportunity to cheat. As some have already mentioned, a dice tower or rolling against some kind of mini wall like in a craps would remove any chance for cheating.

[JonSteitzer]

I love this video, this is so well done, concise, substantive, mathematical

[jacobdavidlet]

My largest problem is that I regularly play with 1 or 2 amateur stage magicians. The more skilled player can roll the die so it results on the better half every time. As long as the table is flat, and there are no obstacles in the way, he will never get a bad roll unless he wants to. Worse yet, we know what he is doing, but he can make it look like a normal roll. The other one can do it too, just not as well. An extreme case, yes, but they can't do it with normal d20's so I have them use that.

[ElBruxon]

Did the math too, have a MTG spin down which I wanted to use, it actually gave a 10.65 percent :)

[JonSteitzer]

This remains the best video on spin down dice versus d20's on the entire internet I wish everyone would see it

[cosmoesis]

Spin downs are more likely to stay on a range then not with spindown then a d20. It's about the spacing of high and low numbers not the number values themselves.
It quiet actually is based on physics and it's super obvious as the roll slows before stopping especially if looking for a range of numbers as opposed to an exact number.

[KonkaBass]

what I submit, after realizing dice are unbalance after checking in a salt water mixture, playing some games, and then thinking on it...is that; is your tablet top made of water? no. the forces at work when you roll a die on any solid tablet top faaaar out weigh any sort of unbalance in a die.

[terriblej]

This is the first I've heard of spin die. That sound great for keeping life since you aren't rolling it. It is only a life tracker. Balance isn't needed